Covalent Bonding & Molecular Orbital TheoryChemistry 754 Solid State Chemistry Dr. Patrick Woodward Lecture #16 References - MO Theory Molecular orbital theory is covered in many places including most general inorganic chemistry texts. The material for this lecture (along with many of the figures) was taken from the following two texts: “Orbital Interactions in Chemistry” Thomas Albright, Jeremy K. Burdett & Myung-Hwan Whangbo, MyungWhangbo, Wiley & Sons, New York (1985). “Chemical Bonding in Solids” Jeremy K. Burdett, Oxford University Press, Oxford (1995). The destabilization of the antibonding MO is always greater than the stabilization of the bonding MO. chalcogenides and halides explain the following coordination preferences: – – – – Cu2+ & Mn3+ → distorted octahedral environment Ni2+ and Fe3+ → regular octahedral environment Pd2+ and Pd2+ → square planar environment Pb2+. Sb3+ → asymmetric coordination environment MO Diagram for H2 The number of MO’s is equal to the number of atomic orbitals. Each MO can hold 2 electrons (with opposite spins). orbitals. Sn2+. The antibonding MO has a nodal plane between atoms and ⊥ to the bond. while Si and Ge are semiconductors? • Why are the π electrons delocalized in benzene (C6H6) and localized in cyclobutadiene (C4H4)? • In oxides. Bi3+. In the diagrams at the top and bottom the solid line denotes the electron density from MO theory and the dashed line the electron density from superimposing to atomic orbitals. E .Questions to Consider • Why is H2O bent rather than linear? Why is NH3 pyramidal rather than planar? • Why are Sn and Pb metals. As the spatial overlap increases ψ1 (bonding MO) is stabilized and ψ2 (antibonding MO) is destabilized. .1st Order MO Diagram for O2 The 2s orbitals have a lower energy than the 2p orbitals. orbitals. This leads to a larger splitting of the bonding and antibonding orbitals. Thus the bond order = 2. orbitals. The mixing becomes more pronounced as the energy separation decreases. and O2 is paramagnetic. The 2px and 2py π-interaction produces to two sets of degenerate orbitals. The MO’s have symmetry descriptors. E 2nd Order MO Diagram for O2 (N2) E A more accurate depiction of the bonding takes into account mixing of of MO’s with the same symmetry (σg+ & σu+). destablized. σg+. Mixing is allowed between MO’s of the MO’ same symmetry. The (σ consequences of this 2nd order effect are: The lower energy orbital is stabilized while the higher energy orbital is destablized. πg. The s and p character of the σ MO’s becomes mixed. In O2 there are 12 valence electrons and each of the 2pπ* orbitals (πg) are 2pπ singly occupied. σu+. The σ-bonds have a greater spatial overlap than the π-bonds. orbitals. πu within point group D∞h. . The orbital character of the more electronegative atom is enhanced in the bonding MO and diminished in the antibonding MO. The splitting between bonding and antibonding MO’s now has an ionic (Ei) (E and a covalent (Ec) component.Heteronuclear Case & Electronegativity E The atomic orbitals of the more electronegative atom are lowered. while the O 2px & 2py orbitals would be non-bonding. (E Ei The ionic component of the splitting (Ei) (E increases as the electronegativity difference increases. The covalency and the covalent stabilization/destabilization decrease as the electronegativity difference increases. Linear AX2 (H2O) MO Diagram In linear H2O the O 2s and O 2pz orbitals could form σ-bonds to H. Walsh Diagram Walsh’s Rule HOMO 2nd Order Jahn-Teller Dist. lowering the energy of the O 2px orbital. . A molecule with a small energy gap between the occupied and unoccupied MO’s is susceptible to a structural distortion that allows intermixing between them. If the HOMO is unperturbed the occupied MO lying closest to it governs the geometrical preference.Bent AX2 (H2O) MO Diagram In bent H2O the O 2s σ∗ orbital and the O 2px orbital are allowed to mix by symmetry. Now there is only one non-bonding orbital (O 2py) Walsh Diagrams & 2nd Order JT Distortions Shows how the MO levels vary as a function of a geometrical change. A molecule adopts the structure that best stabilizes the HOMO. 2 nonbonding O 2p orbitals Actual β-Cristobalite (SiO2) Space Group = I-42d (Tetragonal) Si-O-Si ∠ = 147° Si-O-Si 147° 2” bonding at O2“sp Walsh Diagram for NH3 In the planar (D3h) form the HOMO is a non-bonding O 2p orbital (a2) containing 2 electrons. In the pyramidal (C3v) form the N 2s – H 1s σ* orbital (a1) can mix with the nonbonding O 2p orbital. HOMO .Covalent Bonding & the Structure of Cristobalite Idealized β-Cristobalite (SiO2) Space Group = Fd3m (Cubic) Si-O-Si ∠ = 180° Si-O-Si 180° sp bonding at O2-. Stabilizing the HOMO. C 2p 2s t2* a1* Diamonds and Lead Structure & Properties of the Group 14 Elements 2p 2s a1 Element C Si Ge α-Sn β-Sn Pb Structure Diamond Diamond Diamond Diamond Tetragonal FCC Eg(eV) eV) 5.7 0.Tetrahedral AX4 (CH4) MO Diagram Notice that while both the 2s and 2p orbitals on Carbon are involved in bonding.1 Metal Metal t2 Pb 6p t2* 6p t2 a1* a1 6s 6s As you go proceed down the group the tendency for the s-orbitals s-orbitals to become involved in bonding diminishes.1 0. .5 1. This destabilizes tetrahedral coordination and semiconducting/insulating semiconducting/insulating behavior. in a perfect tetrahedron mixing of the s (a1) and p (t2) orbitals is forbidden. antibonding Pb 6s orbitals. In each system there are n π-MO’s. In C6H6 there is a large HOMOLUMO gap and the e1g orbitals are fully occupied. by mixing with an orbitals. ions adopt a very asymmetric coordination environment. (Tl Sn2+. etc. Benzene (C6H6) Cyclic Polyenes Consider two cyclic CnHn systems. This distortion is similar to the one seen in NH3. The sketches to the left show the phases of the C 2pz orbitals that are responsible for π-interactions. Such mixing is forbidden by symmetry in tetrahedral and octahedral coordination.). The driving force for this is to lower the energy of the filled. The lowest energy orbital has no nodes (all orbitals in phase) while the highest energy state has the maximum number (n/2). empty Pb 6p orbital. In C4H4 the eg orbital HOMO is ½ occupied (triplet ground state). Bi3+. so a distortion to a lower symmetry leading to the formation of the so-called “stereoactive electron lone pair” occurs. Such “stereoactive distortions are common for main group ions with their valence s electrons (Tl+. E Cyclobutadiene (C4H4) . the tetragonal form is shown above) the Pb2+ PbO.2nd Order JT Distortion in PbO Pb 6s HOMO In both polymorphs of PbO (red PbO. Sb3+. but undergoes a distortion to a rectangular shape (D2h). .dyz. d-orbitals. The t2g orbitals (dxy. (π Note that in an octahedron there is no mixing between s. p and d-orbitals. Hence.dy2-y2) are σantibonding.dxz) are π(d antibonding (not shown). in energy since the spatial overlap of the σ-interaction is stronger. This leads to formation of two localized double bonds. C4H4 is said to be antiaromatic. orbitals.1st Order Jahn-Teller Distortion in C4H4 In practice cyclobutadiene does not form a regular square (D4h). For a main group metal the same diagram applies. The latter are higher antibonding. A non-linear molecule with an incompletely filled degenerate HOMO is susceptible to a structural distortion that removes the degeneracy. while the eg orbitals (dz2. Octahedral Coordination The diagram to the left shows a MO diagram for a transition metal octahedrally coordinated by σ-bonding ligands. but we neglect the dorbitals. This stabilizes one of the HOMO’s (which becomes doubly occupied) and destabilizes the other (which becomes empty). (π-bonding has been neglected) ligands. antiaromatic. E 1st Order Jahn-Teller Dist. . orbitals. 2 long + 4 short bonds – stabilizes the dz2 orbital 2 short + 4 long bonds – stabilizes the dx2-y2 orbital . but with Ni2+ the crystal field splitting is usually too small to overcome the spin pairing energy and octahedral coordination results. Transition metals with electron counts that lead to partially filled eg orbitals (HS d4. The Jahn-Teller theorem tells us there should be a distortion when the eg orbitals of a TM octahedral complex are partially occupied. The d8 ions Pd2+ and Pt2+ have a strong preference for sq. d8 & d9 in particular) will be prone to undergo distortions from octahedral toward square planar. Jahn-Teller Distortions: The long and the short of it. To a first approximation two choices give the same energetic stabilization. which stabilizes the dz2 and removes the degeneracy of the eg orbitals. planar coordination. but it doesn’t tell us what type of distortion should occur.Square Planar Coordination The diagram to the left shows a MO diagram for a transition metal in square planar coordination. (π-bonding has been (π neglected) Among the changes the most important is that now the s and dz2 orbitals can mix. such as Hg2+ adopt very large 2 short + 4 long distortions (in many cases the distortion is so large that the coordination is essentially linear).40Å 3.23Å 2.18Å 3. 2 × 2.18Å) and HgBr2 (4 × 3.48Å so? Why do d10 ions distort at all? Jahn-Teller Distortions dz2-s Mixing The empty ns orbital is of appropriate symmetry to mix with the (n-1)dz2 orbital. In contrast d10 ions. and the distortions are usually considerably larger distortion. but not with the (n-1)dx2-y2 orbital. For example consider the bond distances in CuBr2 (4 × 2. In practice Cu2+ (d9) and Mn3+ (HS) almost always take the 2 long + 4 short distortion. Why is this 2.48Å). This dictates the details of the dist. with Cu2+. (2 short + (∆ 4 long favored) .23Å. Long bonds drawn with dotted lines. both of which adopt distorted CdI2 structures.40Å. d9 case (Cu2+): The dz2-s mixing favors preferential occupation of the dz2 orbital (2 long + 4 short favored) d10 case (Hg2+): The dz2-s mixing is largest when the energy separation between the two is minimized (∆E2 > ∆E1).Distortions in d9 & d10 Halides Short bonds drawn with solid lines. 2 × 3.
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